Whenever I palm mute some notes, it always sounds really soft and weak -- almost like a "blump" kind of sound. I've been wanting to get the metal and shorter palm mutes (like this). Even if I use more distortion or change the drive, it almost always stays the same. What exactly is the problem?

well there are a lot of things that can make your mutes sound harder, i think first off using a pick with a nice pointed tip helps, round edged tips tend to slide across or brush over the string
also where you place the palm of your hand, either towards or away from the bridge makes a huge difference, the further you get from the brigde, the tighter it'll sound
using a good noise gate helps to eliminate any ringing in between chugs too
lastly, i think if you want to get a beefier mute, for instance instead of playing the low E on its own, play an E power chord and it'll sound fuller

I'd say that right-hand positioning is 99% of the sound - get it right and you'll be able to play good-sounding mutes on any setup. Two things I'd like to add are: you'll find that downstrokes give a much "chunkier" mute than alternate picking, so you might consider playing the heavier parts with all downstrokes and that adding just a bit of thumb flesh to the pick attack (as in pinch harmonics, but not quite so marked) can do a lot for the aggressiveness of the sound.
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FazaMay 16 '11 at 8:31